The generator matrix

 1  0  0  0  0  1  1  1  0  0  X  1  1  1  X  1  X  X  0  1  1  1  1  1  0  1  X  1  0  1  X  X  1  1  1  1  1  1  1  1  1  0  1  0  X  1  X  X  1  X  1  1  0  0  1  1  0  1  1  0  0  0  1  X  1  X  1  1  1  X  0  1  0  0  0  1  0  1  1  1  0  X  1  X  1  X  1  X  1  0  X  1  0  X  1  1
 0  1  0  0  0  X  1 X+1  1  1  1  1  1  0  X  0  1  1  X  0 X+1  X  1  X  X  1  1  0  0 X+1  1  0 X+1  X  0 X+1  1 X+1  X  0  0  0  1  1  1  X  1  0  0  1 X+1  X  1  0 X+1  X  1 X+1  1  1  1  X  1  1  0  0 X+1  X X+1  X  1  1  X  X  1  X  1  0  0  1  0  1  1  X X+1  1  1  1  0  X  0  0  1  1  1  X
 0  0  1  0  0  0  0  0  X  1  1  1 X+1  1  1 X+1  0 X+1  1  X X+1  1  X  0  0  1  1 X+1  1  0  0  1  X  0 X+1 X+1  X  X X+1  1  X  1  1  1  X  1  0  1  X  X  1  1  0  X  0  1  X  1  1  1 X+1  0  X  1  X  X X+1 X+1 X+1  0 X+1  X  1  1  1 X+1  0 X+1  0  0  1  X  0  0  X  1  0  X  X  0  1  X  1  X  X  1
 0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0 X+1  1 X+1  1 X+1  1 X+1  1  1 X+1 X+1  1 X+1 X+1  1  0  0  X  X  X  X  1 X+1  1  X  1  X  X  1  X  0  X  0  0  1  0 X+1  1  X X+1 X+1  X  1 X+1  X  1  1  1  1  1  X X+1  1  X  0  0  1  0  X  0  X X+1  X X+1  X  X  0  1  X X+1  1  1  X  1  1  0 X+1 X+1 X+1  X
 0  0  0  0  1  1 X+1  X X+1  1  0  X  1  1  1  X  1  X X+1  1  1  0  X  X X+1  0 X+1 X+1  X X+1  0 X+1  0 X+1  1 X+1  1  X  0 X+1  0  X X+1  0  0  1 X+1  0  X  X  1  X  1 X+1  1 X+1  0  0  0 X+1  1  1  X  X  0  X  X  X X+1  1 X+1  0  1  0  X X+1  1 X+1 X+1  0  1  0  1  0  1  X X+1 X+1  X  0  0  0  1 X+1  1  X

generates a code of length 96 over Z2[X]/(X^2) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+82x^89+112x^90+100x^91+43x^92+58x^93+132x^94+72x^95+38x^96+48x^97+58x^98+38x^99+31x^100+34x^101+40x^102+14x^103+9x^104+18x^105+18x^106+12x^107+6x^108+10x^109+14x^110+12x^111+4x^113+6x^114+2x^115+2x^117+2x^118+6x^119+2x^122

The gray image is a linear code over GF(2) with n=192, k=10 and d=89.
This code was found by Heurico 1.16 in 11.4 seconds.